Solo female traveler here. I spent 2 nights at the Isafjordur Hotel on my way to Hornstrandir. If you are planning a stop in Isafjordur, this hotel is possibly the best, if not the only, choice for location and services.
The hotel is a ten minute walk to the Harbor where I boarded a Borea tour. It is also a ten minute walk to a very good seafood restaurant that has quite a following. The location in front of the water is superbly scenic, and the accommodations are more than adequate for a town with about 3000 residents. My room was small, with 2 very small twin beds side by side. It was clean and served the purpose. The bathroom was also quite small and did not have too much in terms of amenities. The breakfast was fine, and the dinner was acceptable as well. I would not give the hotel a 5-star rating, however, I felt that it fulfilled my needs very well. Isafjordur is a lovely town where I felt safe and would certainly recommend this hotel.